.\"	$OpenBSD: EC_GROUP_new.3,v 1.11 2019/08/19 13:08:26 schwarze Exp $
.\"	OpenSSL 9b86974e Mon Aug 17 15:21:33 2015 -0400
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.\" This file was written by Matt Caswell <matt@openssl.org>.
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.Dd $Mdocdate: August 19 2019 $
.Dt EC_GROUP_NEW 3
.Os
.Sh NAME
.Nm EC_GROUP_new ,
.Nm EC_GROUP_free ,
.Nm EC_GROUP_clear_free ,
.Nm EC_GROUP_new_curve_GFp ,
.Nm EC_GROUP_new_curve_GF2m ,
.Nm EC_GROUP_new_by_curve_name ,
.Nm EC_GROUP_set_curve_GFp ,
.Nm EC_GROUP_get_curve_GFp ,
.Nm EC_GROUP_set_curve_GF2m ,
.Nm EC_GROUP_get_curve_GF2m ,
.Nm EC_get_builtin_curves
.Nd create and destroy EC_GROUP objects
.Sh SYNOPSIS
.In openssl/ec.h
.In openssl/bn.h
.Ft EC_GROUP *
.Fo EC_GROUP_new
.Fa "const EC_METHOD *meth"
.Fc
.Ft void
.Fo EC_GROUP_free
.Fa "EC_GROUP *group"
.Fc
.Ft void
.Fo EC_GROUP_clear_free
.Fa "EC_GROUP *group"
.Fc
.Ft EC_GROUP *
.Fo EC_GROUP_new_curve_GFp
.Fa "const BIGNUM *p"
.Fa "const BIGNUM *a"
.Fa "const BIGNUM *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft EC_GROUP *
.Fo EC_GROUP_new_curve_GF2m
.Fa "const BIGNUM *p"
.Fa "const BIGNUM *a"
.Fa "const BIGNUM *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft EC_GROUP *
.Fo EC_GROUP_new_by_curve_name
.Fa "int nid"
.Fc
.Ft int
.Fo EC_GROUP_set_curve_GFp
.Fa "EC_GROUP *group"
.Fa "const BIGNUM *p"
.Fa "const BIGNUM *a"
.Fa "const BIGNUM *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_GROUP_get_curve_GFp
.Fa "const EC_GROUP *group"
.Fa "BIGNUM *p"
.Fa "BIGNUM *a"
.Fa "BIGNUM *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_GROUP_set_curve_GF2m
.Fa "EC_GROUP *group"
.Fa "const BIGNUM *p"
.Fa "const BIGNUM *a"
.Fa "const BIGNUM *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_GROUP_get_curve_GF2m
.Fa "const EC_GROUP *group"
.Fa "BIGNUM *p"
.Fa "BIGNUM *a"
.Fa "BIGNUM *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft size_t
.Fo EC_get_builtin_curves
.Fa "EC_builtin_curve *r"
.Fa "size_t nitems"
.Fc
.Sh DESCRIPTION
The EC library provides functions for performing operations on
elliptic curves over finite fields.
In general, an elliptic curve satisfies an equation of the form:
.Pp
.Dl y^2 = x^3 + ax + b
.Pp
Within the library there are two forms of elliptic curves that are of
interest.
The first form is those defined over the prime field Fp.
The elements of Fp are the integers 0 to p-1, where
.Fa p
is a prime number.
This gives us a revised elliptic curve equation as follows:
.Pp
.Dl y^2 mod p = x^3 + ax + b mod p
.Pp
The second form is those defined over a binary field F2^m where the
elements of the field are integers of length at most m bits.
For this form the elliptic curve equation is modified to:
.Pp
.Dl y^2 + xy = x^3 + ax^2 + b (where b != 0)
.Pp
Operations in a binary field are performed relative to an irreducible
polynomial.
All such curves with OpenSSL use a trinomial or a pentanomial for this
parameter.
.Pp
An
.Vt EC_GROUP
structure is used to represent the definition of an elliptic curve.
A new curve can be constructed by calling
.Fn EC_GROUP_new ,
using the implementation provided by
.Fa meth
(see
.Xr EC_GFp_simple_method 3 ) .
It is then necessary to call either
.Fn EC_GROUP_set_curve_GFp
or
.Fn EC_GROUP_set_curve_GF2m
as appropriate to create a curve defined over Fp or over F2^m, respectively.
.Pp
.Fn EC_GROUP_set_curve_GFp
sets the curve parameters
.Fa p ,
.Fa a ,
and
.Fa b
for a curve over Fp stored in
.Fa group .
.Fn EC_GROUP_get_curve_GFp
obtains the previously set curve parameters.
.Pp
.Fn EC_GROUP_set_curve_GF2m
sets the equivalent curve parameters for a curve over F2^m.
In this case
.Fa p
represents the irreducible polynomial - each bit represents a term in
the polynomial.
Therefore there will either be three or five bits set dependent on
whether the polynomial is a trinomial or a pentanomial.
.Fn EC_GROUP_get_curve_GF2m
obtains the previously set curve parameters.
.Pp
The functions
.Fn EC_GROUP_new_curve_GFp
and
.Fn EC_GROUP_new_curve_GF2m
are shortcuts for calling
.Fn EC_GROUP_new
and the appropriate
.Fn EC_GROUP_set_curve_*
function.
An appropriate default implementation method will be used.
.Pp
Whilst the library can be used to create any curve using the functions
described above, there are also a number of predefined curves that are
available.
In order to obtain a list of all of the predefined curves, call the
function
.Fn EC_get_builtin_curves .
The parameter
.Fa r
should be an array of
.Vt EC_builtin_cure
structures of size
.Fa nitems .
The function will populate the
.Fa r
array with information about the builtin curves.
If
.Fa nitems
is less than the total number of curves available, then the first
.Fa nitems
curves will be returned.
Otherwise the total number of curves will be provided.
The return value is the total number of curves available (whether that
number has been populated in
.Fa r
or not).
Passing a
.Dv NULL
.Fa r ,
or setting
.Fa nitems
to 0, will do nothing other than return the total number of curves
available.
The
.Vt EC_builtin_curve
structure is defined as follows:
.Bd -literal
typedef struct {
	int nid;
	const char *comment;
} EC_builtin_curve;
.Ed
.Pp
Each
.Vt EC_builtin_curve
item has a unique integer ID
.Pq Fa nid
and a human readable comment string describing the curve.
.Pp
In order to construct a builtin curve use the function
.Fn EC_GROUP_new_by_curve_name
and provide the
.Fa nid
of the curve to be constructed.
.Pp
.Fn EC_GROUP_free
frees the memory associated with the
.Vt EC_GROUP .
If
.Fa group
is a
.Dv NULL
pointer, no action occurs.
.Pp
.Fn EC_GROUP_clear_free
destroys any sensitive data held within the
.Vt EC_GROUP
and then frees its memory.
If
.Fa group
is a
.Dv NULL
pointer, no action occurs.
.Sh RETURN VALUES
All
.Fn EC_GROUP_new*
functions return a pointer to the newly constructed group or
.Dv NULL
on error.
.Pp
.Fn EC_get_builtin_curves
returns the number of builtin curves that are available.
.Pp
.Fn EC_GROUP_set_curve_GFp ,
.Fn EC_GROUP_get_curve_GFp ,
.Fn EC_GROUP_set_curve_GF2m ,
and
.Fn EC_GROUP_get_curve_GF2m
return 1 on success or 0 on error.
.Sh SEE ALSO
.Xr crypto 3 ,
.Xr d2i_ECPKParameters 3 ,
.Xr EC_GFp_simple_method 3 ,
.Xr EC_GROUP_copy 3 ,
.Xr EC_KEY_new 3 ,
.Xr EC_POINT_add 3 ,
.Xr EC_POINT_new 3 ,
.Xr ECDH_compute_key 3 ,
.Xr ECDSA_SIG_new 3
.Sh HISTORY
.Fn EC_GROUP_new ,
.Fn EC_GROUP_free ,
.Fn EC_GROUP_clear_free ,
.Fn EC_GROUP_new_curve_GFp ,
.Fn EC_GROUP_set_curve_GFp ,
and
.Fn EC_GROUP_get_curve_GFp
first appeared in OpenSSL 0.9.7 and have been available since
.Ox 3.2 .
.Pp
.Fn EC_GROUP_new_curve_GF2m ,
.Fn EC_GROUP_new_by_curve_name ,
.Fn EC_GROUP_set_curve_GF2m ,
.Fn EC_GROUP_get_curve_GF2m ,
and
.Fn EC_get_builtin_curves
first appeared in OpenSSL 0.9.8 and have been available since
.Ox 4.5 .
